Therefore, if Δ x is small, then Δ y ≈ f′( x 0)Δ x (the wavy lines mean “is approximately equal to”). Because the derivative is defined as the limit, the closer Δ x is to 0, the closer will be the quotient to the derivative. The derivative of a function at the point x 0, written as f′( x 0), is defined as the limit as Δ x approaches 0 of the quotient Δ y/Δ x, in which Δ y is f( x 0 + Δ x) − f( x 0).

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